Browsing by Author "Jiménez Urroz, Jorge"

Cropping Euler factors of modular Lfunctions
González Rovira, Josep; Jiménez Urroz, Jorge; Lario Loyo, Joan Carles (201309)
Article
Open AccessAccording to the Birch and SwinnertonDyer conjectures, if A/Q is an abelian variety, then its Lfunction must capture a substantial part of the properties of A. The smallest number field L where A has all its endomorphisms ... 
Modular forms with large coefficient fields via congruences
Dieulefait, Luis; Jiménez Urroz, Jorge; Ribet, Keneth (Springer, 20150501)
Article
Open AccessWe use the theory of congruences between modular forms to prove the existence of newforms with squarefree level having a fixed number of prime factors such that the degree of their coefficient fields is arbitrarily large. ... 
On fields of definition of torsion points of elliptic curves with complex multiplication
Dieulefait, Luis Victor; Gonzalez Jimenez, Enrique; Jiménez Urroz, Jorge (201106)
Article
Open AccessFor any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of ... 
Orders of CM elliptic curves modulo p with at most two primes
Iwaniec, H.; Jiménez Urroz, Jorge (2010)
Article
Restricted access  publisher's policyNowadays the generation of cryptosystems requires two main aspects. First the security, and then the size of the keys involved in the construction and comunication process. About the former one needs a di±cult ... 
Orders of CM elliptic curves modulo p with at most two primes
Iwaniec, Henryk; Jiménez Urroz, Jorge (2006)
Article
Open AccessWe prove the analog of Koblitz conjecture when replacing primes by almost prime numbers and considering elliptic curves with complex multiplication. In other words for infinitely many primes $p$, (given in a quantitative ... 
Small primitive roots and malleability of RSA
Jiménez Urroz, Jorge; Dieulefait, Luis Victor (2012)
Conference report
Open AccessIn their paper [9], P. Paillier and J. Villar make a conjectur e about the malleability of an RSA modulus. In this paper we present an ex plicit algo rithm refuting the conjecture. Concretely we can factorize an RSA ... 
Squarefree discriminants of Frobenius rings
David, Chantal; Jiménez Urroz, Jorge (201009)
Article
Open AccessLet E be an elliptic curve over Q. It is well known that the ring of endomorphisms of $E_p$, the reduction of E modulo a prime p of ordinary reduction, is an order of the quadratic imaginary field $Q(\pi_p)$ generated ...